When Harriet Harman was nearing the end of her time at university, a male tutor took her aside for a chat. If she slept with him, he explained, she’d get a 2:1. But otherwise – well, her case was borderline.

Repulsed, she refused (and thankfully got the 2:1 anyway). But years later, she learned that he’d tried the same trick on another student, one from a less wealthy background than Harman’s, who knew all her family’s hopes were pinned on her succeeding. The other girl, wretchedly, had not dared refuse. The story is a striking lesson not merely about the abuse of power, but the protection sometimes unfairly afforded by privilege. And if you think things like this don’t happen nowadays, then you probably need to read this book.

If I had a teenage daughter, especially one who didn’t see the point of politics, this is the book I’d buy her. Chatty, accessible and occasionally eye‑opening, it’s a history of the things conventional political memoirs miss out – written by someone who built a career on things conventional politicians missed out.

Admittedly, it’s disconcerting at first to see seminal events in Labour history – Iraq, the transition from Blair to Brown, the rise of Jeremy Corbyn – briskly dispatched in a few pages. And since Harman never kept a diary there are none of those exhaustive (and exhausting) accounts political junkies adore, detailing which aide said what to whom in which crisis meeting. But for lay readers, that’s a bonus. What we get instead are human moments that stick in the mind, plus a lively account of the one subject most political memoir writers know next to nothing about: how it felt to be a woman working in one of the least forgiving (and when she was elected in 1982, most macho) careers around.

The depths of her struggle with maternal guilt will surprise some. Pregnant when a byelection unexpectedly cropped up in the seat she hadn’t expected to fight so early, Harman had two more children while rising up the opposition ranks. She writes beautifully of her longing to be with her babies, and the nagging feeling that because she wasn’t part of the school gate crowd she must be doing it all wrong. (The letters she got, arguing that running for parliament made her an unfit mother, can’t have helped.)

But to admit she was struggling would have damaged her, so she pushed on, pretending to be coping well, “fearing that any sign that I wasn’t would unleash a torrent of accusations that I wasn’t doing my job properly”. There is a telling anecdote about how, having promised to take her son for a half-term treat, she declined a last-minute request to cover for a colleague in parliament. Summoned by her then boss, Robin Cook, to explain herself, she didn’t dare admit the truth and simply refused to say where she’d been – at which point he instantly forgave her, assuming she must be sneaking around having an illicit affair. Bunking off to see the children would have been unforgivable but going awol for sex simply made you one of the gang.

If the intensity of her maternal feelings made life difficult for Harman personally, however, they made it easier for women she will never meet – they drove her campaigns for better childcare, extended rights at work and a critical mass of women in politics. Safety, perhaps, in numbers.

Her struggles with maternal guilt will surprise some. She writes beautifully of her longing to be with her babies

Yet even after a long and successful career, there are clearly scores to settle. She is brutal about Peter Mandelson, suggesting he could have done more to unite Brown and Blair but that it wasn’t in his interests to do so (after all, when they were getting on they didn’t need him so much). Neither John Prescott nor David Miliband emerge well, and while she writes fondly of both Brown and Blair, some slights still rankle. She recounts one almost farcical encounter with Brown, in which he asked her to defend him publicly against charges of using women as window dressing, while refusing to give her, his elected deputy leader, the cabinet post that would make her title meaningful. No wonder Barbara Castle tells her over tea that “all prime ministers are bastards” at least occasionally.

But the consolation for all the times she doesn’t seem to have been taken seriously inside government is the support of ordinary women outside. Harman realised early that the more she ruffled feathers, “the more women would write to me, or come up to me in the street, and say, ‘That happened to me too. Keep at it.’” Fired as secretary of state for social security after an unhappy year of fighting with her deputy, Frank Field – who had been Blair’s first choice for the job – she began a project interviewing low-paid women in factories about their working lives. Their experiences formed the basis of her successful case for extending maternity leave, and earned her a path back into government. (After Labour lost power, she led a similar project with older women, uncovering a forgotten group furious at being treated as if they were invisible to employers; this time, one feels there is unfinished business for somebody else to pick up.)

Harman at home with her children in 1988. Photograph: Rex shutterstock

Yet despite twice serving as Labour’s temporary leader, after the resignations of Brown and Miliband, she never tried to capitalise on her late-blooming popularity and run for leader. Some will say, of course, that she wouldn’t have been up to it. But lesser politicians in all parties have run for (and occasionally got) the top job. She argues simply that when the children were younger it was hard enough just to stay afloat, and by the time they had grown up the moment had passed. And besides, “having been denigrated in the press and certainly not seen as leadership material, it’s perhaps not surprising that this wasn’t how I saw myself”.

Imagine, then, how it feels to see the equally denigrated Corbyn run and win. To her he is a “painful echo” of what was wrong with Labour in the 1980s, when in her words the party became “an angry minority. At the weekends, we’d be marching and demonstrating, while most people were doing things like going shopping, taking the kids to football.” Voters simply concluded they must be on a different planet. It’s a grimly familiar story.

Indeed, much of the history here is grimly familiar, from tales of physical intimidation in party meetings to an unfurling NHS crisis under a Conservative government. As a shadow health minister in the 1990s, Harman recalls a cardiac surgeon showing her a list of patients waiting for surgery. Two thirds would die, he said, before he could operate; completely avoidable deaths, if the waiting list wasn’t so long. It is a salutary lesson in the impotence of opposition but also a warning to a new generation of Labour activists that things may get worse before getting better.

Yet the book ends on an upbeat tone, with a feminist manifesto distilled from 40 years of struggle that feels uncannily contemporary, especially following the Women’s March against Trump. Be gratified at progress made, she advises, but never grateful; you’re only getting what you should always have had. Support other women, work with men but don’t let them take over, and don’t panic when vested interests bite back: “If you are not having arguments, you are not making a difference.” Amen.

•A Woman’s Work is published by Allen Lane. To order a copy for £15 (RRP £20) go to bookshop.theguardian.com or call 0330 333 6846. Free UK p&p over £10, online orders only. Phone orders min p&p of £1.99.